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Spline Functions: Basic Theory

Larry Schumaker's Spline Functions was first published in 1981, then in a second edition with minor changes in 1993. The 1981 Telegraphic Review described the book as

A detailed and comprehensive introduction to the theory of polynomial, generalized, and multidimensional splines emphasizing their algebraic, analytic, and approximation-theoretic properties.

For much more information about the book, see the review in the Bulletin of the AMS, 6 (2) (1982), 238-247.

This new edition, in the Cambridge Mathematical Library series, is basically a reprint of the second edition enriched by a "Supplement" that reports on progress since then. The supplement is 23 pages long and comes with a 17-page bibliography.